Steady-state computer simulations can provide insight into how physical stochastic processes operate. Any insight gained through such computer simulations is valuable because stochastic processes abound within commercial industries (e.g., assessment of long-run average performance measures associated with operating an automotive assembly line) as well as other industries (e.g., financial industries with the ever varying fluctuations of stock and bond prices). Complicated statistical issues can arise when attempting to analyze stochastic output that has been generated from a steady-state simulation. As an illustration, a difficulty can arise as to how to provide statistically valid confidence intervals for the steady-state mean (or other statistic) of the simulation's output.